Exercise
$\csc^2\left(x\right)\cdot\cos^2\left(x\right)=\cot^2-\cos^2$
Step-by-step Solution
Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation csc(x)^2cos(x)^2=cot(x)^2-cos(x)^2. Simplify \csc\left(x\right)^2\cos\left(x\right)^2 into \cot\left(x\right)^2 by applying trigonometric identities. Group the terms of the equation by moving the terms that have the variable x to the left side, and those that do not have it to the right side. Cancel like terms \cot\left(x\right)^2 and -\cot\left(x\right)^2. Removing the variable's exponent raising both sides of the equation to the power of \frac{1}{2}.
Solve the trigonometric equation csc(x)^2cos(x)^2=cot(x)^2-cos(x)^2
Final answer to the exercise
$x=\frac{1}{2}\pi+2\pi n,\:x=\frac{3}{2}\pi+2\pi n\:,\:\:n\in\Z$